I have a feeling that diagnostics might be at a premium in your neighborhood.

I really doubt a coil, the crank sensor is a possibility, they are often heat affected, but the description of the problem sounds more like a fuel thing.

The first step in diagnostics is to see whether the problem is fuel or spark related. I would do a fuel pressure/volume test first, but that probably isn't practical. One simple suggestion, take the line from where it supplies fuel to the fuel distributor. The line attaches to a fitting which then screws into the fuel distributor. There is a screen in the fitting. Take the fitting out and verify that it is clear.

I don't know what ignition is in your car but if you can put a plug into a plug wire end and sit it on the engine and crank you can verify the intensity of the spark by increasing the plug gap. You should have a spark that you can both see and hear. It should jump even if the electrode is removed (it should jump to the base or edge). DO NOT HOLD it.

After re-reading this I realize that I'm not sure you have a KE system. If it is electronic fuel injection the fitting thing wouldn't apply. I might look to an OVP problem if it is EFI (electronic fuel inection). The OVP will not keep a KE car from restarting (it can cause a stall though and they are heat affected).